Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises: 33

Answer

Any of: $4\sin x\cos x(1-2\sin^{2}x)$ $4\sin x\cos x(\cos^{2}x-\sin^{2}x)$ $4\sin x\cos x(2\cos^{2}x- 1)$

Work Step by Step

$\sin 4x=\sin[2(2x)] =$ ... Double-Angle identity $...\sin 2A=2\sin A\cos A$ $=2\sin 2x\cos 2x$ ... Double-Angle ... $\sin 2A=2\sin A\cos A$ ... $\cos 2A=1-2\sin^{2}A$ $=2(2\sin x\cos x)(1-2\sin^{2}x)$ $=4\sin x\cos x(1-2\sin^{2}x)$ (answers may differ if other double angle identities for cosine are chosen, $\cos 2A=\cos^{2}A-\sin^{2}A$, $\cos 2A=2\cos^{2}A- 1$) Answer: any of $4\sin x\cos x(1-2\sin^{2}x)$ $4\sin x\cos x(\cos^{2}x-\sin^{2}x)$ $4\sin x\cos x(2\cos^{2}x- 1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.